Why convexity shows up after duration
Many Level I candidates feel that duration should already finish the job. If duration measures interest-rate sensitivity, why add another statistic?
The reason is that duration is a line approximation. It treats the bond price-yield relationship as if it were straight over the relevant interval. Real bond prices do not move in a straight line as yields change. The curve bends, and that bend is convexity.
On the exam, this matters whenever:
- the yield move is not tiny
- two portfolios have similar duration but different cash-flow dispersion
- the vignette compares a barbell and a bullet
- the answer choices ask which bond benefits more from rate volatility
flowchart TD
A["Start with price sensitivity"] --> B{"Is the rate move very small?"}
B -->|Yes| C["Duration may be enough"]
B -->|No| D["Add convexity to refine the estimate"]
C --> E{"Comparing two portfolios with same duration?"}
D --> E
E -->|No| F["Use duration + convexity estimate"]
E -->|Yes| G["Check cash-flow dispersion and convexity"]
G --> H["Barbell usually has more convexity than bullet at same duration"]
Duration gives slope, convexity gives curvature
Modified duration tells you the approximate percentage price change for a small change in yield. Convexity improves that estimate because it captures how the slope itself changes as yields move.